Simplify the following expression: $t = \dfrac{-7r^2 + 35r + 168}{r + 3} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-7$ , so we can rewrite the expression: $ t =\dfrac{-7(r^2 - 5r - 24)}{r + 3} $ Then we factor the remaining polynomial: $r^2 {-5}r {-24} $ ${3} {-8} = {-5}$ ${3} \times {-8} = {-24}$ $ (r + {3}) (r {-8}) $ This gives us a factored expression: $\dfrac{-7(r + {3}) (r {-8})}{r + 3}$ We can divide the numerator and denominator by $(r - 3)$ on condition that $r \neq -3$ Therefore $t = -7(r - 8); r \neq -3$